Let
be a continuous function with
for every continuous function g : [ a , b ] → R {\displaystyle {}g\colon [a,b]\rightarrow \mathbb {R} } . Show f = 0 {\displaystyle {}f=0} .
![{\displaystyle f\colon [a,b]\longrightarrow \mathbb {R} }](https://wikimedia.org/api/rest_v1/media/math/render/svg/6bda17a8ca7ea71906b37514dd0342131a206a98)
![{\displaystyle {}g\colon [a,b]\rightarrow \mathbb {R} }](https://wikimedia.org/api/rest_v1/media/math/render/svg/6b0b133363d20a27f8992d943e5dacad50ae24ba)
.
Show
.
